Optical system for effecting increased irradiance in peripheral area of object

ABSTRACT

Disclosed is a novel optical system for illuminating an object which provides an increased irradiance in the peripheral area of the object. The optical system includes a light source, an entrance pupil for receiving light from the light source, an exit pupil for passing the light received to the object, and an optical axis which extends through the optical system to the light source and the object, respectively, wherein the relationship among the incident height h to the entrance pupil, an illumination height H on the object, and a changing rate (dh/dH) of the incident height and the illumination height is defined by a function, f(H)=(h/H)(dh/dH). The optical system is designed so as to satisfy the following formula in the peripheral area of the object: f(0)&lt;f(H). The function f(0) is represented by f(0)=[fa&#39;/(a&#39;-f)b&#39;}] 2 , where a&#39; is a distance between the light source and the primary principal point of the optical system, and b&#39; is a distance between the real image of the light source and the object.

BACKGROUND OF THE INVENTION

The present invention relates generally to a novel optical system, andparticularly to an optical system which provides light of increasedintensity in the peripheral area of an object to be illuminated so thatit is particularly useful for an illumination system or a projectionsystem applicable to exposure of printed circuit boards, integratedcircuits or the like, for exposure systems applicable to contactexposure apparatus for plate making, step-and-repeat machines or thelike, and for illumination systems applicable to copy machines or thelike.

It is well known that a conventional relay condenser optical system suchas shown in FIG. 1 has been used in an illumination system which isintended to provide uniform illumination light for an entire object areaeffectively. The conventional condenser optical system, referring toFIG. 1, comprises a condenser lens C and a field lens F. The condenseroptical system is designed so that the real image of a light source LS,which is s placed in front of the condenser lens C, is formed adjacentto the field lens F, and the real image of an entrance pupil A of thecondenser lens C is formed on an object S which is placed behind thefield lens F.

The conventional condenser optical system, however, raises a seriousproblem, i.e. the irradiance in the peripheral area of the object isreduced, as shown in FIG. 2, in accordance with the cosine fourth law.For instance, referring to FIG. 1, the irradiance at the point of theobject where the exit angle θ is 27 degrees relative to the optical axisis less than that at the point on the optical axis, i.e. the point wherethe exit angle θ is zero degrees.

There are several reasons, other than the above-mentioned cosine fourthlaw, for the occurrence of irradiance reduction in the peripheral areaof the object, which will be discussed in detail later. Actually, theirradiance in the peripheral area of the object is reduced less than avalue derived from the cosine fourth law. According to the simulationcalculation made by applying lens data listed in Table 1 to the opticalsystem shown in FIG. 1, it is found that the irradiance at the pointwhere the exit angle θ is 27 degrees, is reduced by 50 percent incomparison with the irradiance at the center thereof.

                  TABLE 1                                                         ______________________________________                                               r            d      n                                                  ______________________________________                                        1        0.77           0.37   1.5                                            2        ∞        0.46                                                  3        0.77           0.37   1.5                                            4        ∞                                                              ______________________________________                                         f = 1,                                                                        distance from the light source = 50,                                          distance from the object = 100                                           

FIG. 3 shows an irradiance distribution on the object P, which isobtained by using the optical system shown in FIG. 1, in the case wherea point source is positioned on the optical axis at the distance of 50units away from the optical system. FIG. 4 shows an irradiancedistribution of the meridional ray on the object P, and FIG. 5 shows anirradiance distribution of the sagittal ray on the object P, in each ofwhich the point source is positioned away by 14 units from the opticalaxis and at a distance of 50 units from the optical system. Therespective vertical axis of FIGS. 3 through 5 depicts a relativeirradiance, in which the irradiance of the center of the object P isregarded as 100 percent when the point source is positioned on theoptical axis. On the other hand, the respective horizontal axis of FIGS.3 through 5 depicts a position on the object P. In FIGS. 3 through 5,the position denoted by 50 units corresponds to the position on whichthe exit light from the optical system is impinged.

As mentioned above, the irradiance in the peripheral area of the objectP is actually reduced less than a value derived from cosine fourth law.One of the reasons therefor is an aberration, because the cosine fourthlaw is on the premise that an optical system has no aberration, whereasan actual optical system inevitably has some aberration.

It has then conventionally been practiced that an optical system isdesigned so that the aberration should be eliminated as far as possible,in other words it has commonly been practiced that an optical system isdesigned so as to satisfy the sine condition. Thus, even in anillumination system, the optical system for use in illumination hasconventionally been designed so as to satisfy the sine condition,because it has been believed to be matter of course by a person skilledin the art.

It has been found by the inventors, however, that designing an opticalsystem so as to satisfy the sine condition causes an irradiancereduction in the peripheral area of the object to be illuminated.

Now the reasons why there is irradiance reduction in the peripheral areaof the object will be discussed.

Referring to FIG. 6, which is a schematic view of an optical system,light emitted from the light source LS enters into the optical system atthe entrance height h, in this case the light source LS can be regardedas being placed at an infinite distance from the optical system, becauseit is positioned at a far distance from the optical system in comparisonwith the focal length thereof. The real image of the light source LS isformed at a point I, and the light goes through an exit pupil at an exitangle θ. Satisfying the sine condition means that the sine of the exitangle θ is proportioned to the entrance height h; accordingly therelation can be expressed by the following formula (1):

    h=k.sub.1 ·sin θ                            (1)

where k₁ is a proportional constant.

The light which entered into the optical system at the entrance height hexits therefrom to impinge upon the point Q of the object P. Then, sin θcan be expressed by the following formula (2): ##EQU1## where H is thedistance between the point Q and the center of the object P (hereinafterreferred to as illumination height), and a is the distance between thepoint I and the point Q.

It can then be transformed from the formulae (1) and (2), as follows:##EQU2##

As can be understood from FIG. 6, when the incident height h isincreased, the exit angle θ will become large, hence the illuminationheight H will be increased in accordance therewith, and similarly thedistance a between the point I and the point Q will also be increased.In the case where the entrance height h is increased at a constant rate,the illumination height H will be rapidly increased more than theincrease of the entrance height h, since the illumination height H isproportioned to the product of the distance a and the incident height h,as can be seen from the formula (3). The relationship between theincident light radius A₀ around the optical axis in the entrance pupil Aand the radius P₀ of the illumination area of the object P, similarly tothe relationship between the incident height h and the illuminationheight H, is that the radius P₀ increases at a greater rate than therate at which the radius A increases, from which it will be apparentthat the irradiance on the object P will be reduced as it goes away fromthe optical axis, in comparison with that on the entrance pupil A.

Indeed in an image-formation optical system design it will be necessaryto design the optical system so as to satisfy the sine condition becauseit is important to minimize the aberration, but in an illuminationoptical system design there is no need to do so. Furthermore, designingto satisfy the sine condition causes the irradiance reduction in theperipheral area of the object to be illuminated, as mentioned above.

In a conventional illumination system, it has been practiced, in orderto correct the irradiance reduction in the peripheral area of theobject, that a gradient filter is placed in the optical path thereof, orthat the light source is placed at a sufficient distance from theobject. These conventional correction methods are, however,disadvantageous in view of the fact that light quantity is considerablyreduced in the entire area of the object in the former method, and thatthe illumination system inevitably becomes large in size in the latter.

Furthermore, it may often be required that irradiance in the peripheralarea of an object is increased in comparison with that at the centerthereof. For instance, in the case where an illumination apparatus whenemploying a projection lens is placed optically behind an original to bereproduced, an image projected on a photosensitive material will beaffected by the cosine fourth law even if uniform irradiance is giventhroughout the original.

SUMMARY OF THE INVENTION

It is a principal object of the present invention to provide a noveloptical system particularly useful for an illumination system.

It is another object to provide an optical system which provides anillumination on an object with increased irradiance in the peripheralarea of the object.

It is a further object to provide an optical system adaptable forilluminating a considerably large-scaled object, e.g. 900 mm by 900 mm.

The aforementioned objects are accomplished by the present invention,with an optical system which includes a light source, an entrance pupilfor receiving light from the light source, an exit pupil for passing thelight received to the object, and an optical axis which extends to thelight source and the object, respectively, through the optical system,wherein the relationship among an incident height h to the entrancepupil, an illumination height H on the object and a changing rate(dh/dH) of the incident height and the illumination height is defined bya function, f(H)=(h/H) (dh/dH), the optical system being designed so asto satisfy the following formula in the peripheral area of the object:f(0)<f(H), f(0) being represented by the formula:f(0)=[fa'/{(a'-f)b'}]², where a' is a distance between the light sourceand the primary principal point of the optical system, and b' is adistance between the real image of the light source and the object.

According to another feature of the present invention, the opticalsystem comprises three optical units, the first optical unit including apositive lens and having a convex rear surface, the second optical unitincluding a positive lens and having a convex front surface, the thirdoptical unit including either a positive or negative lens and having aconvex rear surface, the optical system satisfying the followingformulae:

    ______________________________________                                        -0.3f < f.sub.F <0.3f                                                                              (13)                                                     0.4 < (1 - n.sub.5)f/r.sub.6                                                                       (14)                                                     -0.6f < f.sub.B < 0.1f                                                                             (15)                                                     0.04 < (1 - n.sub.1)f/r.sub.2 < 0.8                                                                (16)                                                     (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 <0                                                   (17)                                                     ______________________________________                                    

where f is the synthesized focal point of the optical system; f_(F) is adistance between the front surface of the first optical unit and theprimary focal point of the optical system; f_(B) is a distance betweenthe rear surface of the third optical unit and the secondary focal pointof the optical system; n₁, n₃ and n₅ are respectively the refractiveindex of the first, second and third optical units; r₂ and r₄ arerespectively the radius of curvature of the rear surfaces of the firstand second optical units; and r₅ and r₆ are respectively the radius ofcurvature of the front and rear surfaces of the third optical unit.

According to a further feature of the present invention, the opticalsystem comprises four optical units, the first optical unit including apositive lens and having a convex rear surface, the second optical unitincluding either a positive or negative lens and having a convex rearsurface, the third optical unit including a positive lens and having aconvex front surface, the fourth optical unit including a positive lensand having a convex rear surface, the synthesized focal length of boththe first and second optical units being positive, the optical systemsatisfying the following formulae:

    0.8≦{(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f   (58)

    0.75f≦F.sub.3.4 ≦1.52f                       (59)

where f is a synthesized focal length of the optical system; f₃.4 is asynthesized focal length of both the third and fourth optical units; n₅and n₇ are respectively the refractive index of the third and fourthoptical units; and r₅ and r₈ are respectively the radius of curvature ofthe third and fourth optical units.

Further, according to a further feature of the present invention, theoptical system comprises two optical units, the first optical unitincluding a positive lens and having a convex rear surface, the secondoptical unit including a positive lens and having convex front and rearsurfaces, the optical system satisfying the following formulea:

    -0.3≦(d.sub.3 /r.sub.4)≦-0.3                 (76)

    1.0f≦f.sub.2 ≦1.55f                          (77)

where f is a synthesized focal length of the optical system; f₂ is thefocal length of the second optical unit; d₃ is the thickness of thesecond optical unit; and r₄ is the radius of curvature of the rearsurface of the second optical unit.

According to a further feature of the invention, the optical systemcomprises two optical units, the first optical unit including a positivelens and having a convex rear surface, the second optical unit includinga positive lens and having a concave front surface and a convex rearsurface, the optical system satisfying the following formulae:

    -0.68≦{(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f≦0.90 (90)

    0.67≦{(1-n.sub.3)/r.sub.4 }f                        (91)

where f is the synthesized focal length of the optical system; r₂, r₃and r₄ are the radius of curvature of the rear surface of the firstoptical unit and of the front and rear surfaces of the second opticalunit, respectively; and n₁ and n₃ are refractive indexes of the firstand second optical units.

The optical system is preferably formed into so called a fly's eyeconfiguration.

Having the aforementioned features, the present invention has thefollowing useful advantages:

The optical system according to the present invention effectivelyresolves the irradiance reduction caused by the cosine fourth law and/orvignetting in the peripheral area of an object to be illuminated.

The optical system instead increases the irradiance in the peripheralarea of an object to be illuminated, which fact reveals that the opticalsystem is particularly useful in the case where the image of the objectis in turn projected onto e.g. a photosensitive material. The resultantirradiance distribution on the photosensitive material can be ensured tobe uniform throughout the entire surface thereof.

The optical system according to the present invention is accordinglyadaptable for illuminating a considerably large-scaled object.

Other novel features and advantages of the invention will becomeapparent in the course of the following detailed description takentogether with the accompanying drawings, which are directed only to theunderstanding of the present invention and not to the restriction of thescope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an elevational view of a conventional optical system;

FIG. 2 is a graphic representation which shows irradiance distributionof the conventional optical system;

FIGS. 3 through 5 are respectively graphic representations of theirradiance distribution on the object, when using the conventionaloptical system;

FIG. 6 is a schematic elevational view of the conventional opticalsystem;

FIG. 7 is a graphic representation which shows the relationship betweenthe entrance height and the illumination height;

FIG. 8 is a schematic view of an illumination apparatus according to thepresent invention;

FIG. 9 is a schematic view of an illumination apparatus according topresent invention;

FIG. 10 is a side view of lenses forming the optical system;

FIGS. 11-(A) through 11-(C) are graphic representations showing anirradiance distribution on an object;

FIG. 12 is a side view of lenses forming the optical system;

FIGS. 13-(A) through 13-(C) are graphic representations showing anirradiance distribution on an object;

FIG. 14 is a side view of lenses forming the optical system;

FIGS. 15-(A) through 15-(C) are graphic representations showing anirradiance distribution on an object;

FIG. 16 is a side view of lenses forming the optical system;

FIGS. 17-(A) through 17-(C) are graphic representations showing anirradiance distribution on an object;

FIG. 18 is a side view of lenses forming the optical system;

FIGS. 19-(A) through 19-(C) are graphic representations showing anirradiance distribution on an object;

FIG. 20 is a side view of a lens forming the optical system;

FIGS. 21-(A) through 21-(C) are graphic representations showing anirradiance distribution on an object;

FIG. 22 is a side view of lenses forming the optical system;

FIGS. 23 and 24 are explanatory side views showing light rays passingthrough the optical system;

FIG. 25 is a graphic representation showing an irradiance distributionon an object;

FIG. 26 is a side view of lenses forming the optical system;

FIG. 27 is a graphic representation showing an irradiance distributionon an object;

FIG. 28 is a side view of lenses forming the optical system;

FIG. 29 is a graphic representation showing an irradiance distributionon an object;

FIG. 30 is a side view of lenses forming the optical system;

FIG. 31 is a graphic representation showing an irradiance distributionon an object;

FIG. 32 is a side view of lenses forming the optical system;

FIG. 33 is a graphic representation showing an irradiance distributionon an object;

FIG. 34 is a side view of lenses forming the optical system;

FIG. 35 is a graphic representation showing an irradiance distributionon an object;

FIG. 36 is a side view of lenses forming the optical system;

FIG. 37 is a graphic representation showing an irradiance distributionon an object;

FIG. 38 is a side view of lenses forming the optical system;

FIG. 39 is a graphic representation showing an irradiance distributionon an object;

FIG. 40 is a side view of a lens forming the optical system;

FIGS. 41 and 42 are explanatory side views of the light rays passingthrough the optical system;

FIG. 43 is a graphic representation showing an irradiance distributionon an object;

FIG. 44 is a side view of lenses forming the optical system;

FIG. 45 is a graphic representation showing an irradiance distributionon an object;

FIG. 46 is a side view of lenses forming the optical system;

FIG. 47 is a graphic representation showing an irradiance distributionon an object;

FIG. 48 is a side view of lenses forming the optical system;

FIG. 49 is a graphic representation showing an irradiance distributionon an object;

FIG. 50 is a side view of lenses forming the optical system;

FIG. 51 is a graphic representation showing an irradiance distributionon an object;

FIG. 52 is a side view of lenses forming the optical system;

FIG. 53 is a graphic representation showing an irradiance distributionon an object;

FIG. 54 is a side view of lenses forming the optical system;

FIGS. 55 and 56 are explanatory side views showing the light rayspassing through the optical system;

FIG. 57 is a graphic representation showing an irradiance distributionon a object;

FIG. 58 is a side view of lenses forming the optical system;

FIG. 59 is a graphic representation showing an irradiance distributionon an object;

FIG. 60 is a side view of lenses forming the optical system;

FIG. 61 is a graphic representation showing an irradiance distributionon an object;

FIG. 62 is a side view of lenses forming the optical system;

FIG. 63 is a graphic representation showing an irradiance distributionon an object;

FIG. 64 is a side view of lenses forming the optical system;

FIG. 65 is a graphic representation showing an irradiance distributionon an object;

FIG. 66 is a side view of lenses forming the optical system;

FIG. 67 is a graphic representation showing an irradiance distributionon an object;

FIG. 68 is a side view of lenses forming the optical system;

FIGS. 69 and 70 are explanatory side views showing the light rayspassing through the optical system;

FIG. 71 is a graphic representation showing an irradiance distributionon an object;

FIG. 72 is a side view of lenses forming the optical system;

FIG. 73 is a graphic representation showing an irradiance distributionon an object;

FIG. 74 is a side view of lenses forming the optical system;

FIG. 75 is a graphic representation showing an irradiance distributionon an object;

FIG. 76 is a side view of lenses forming the optical system;

FIG. 77 is a graphic representation showing an irradiance distributionon an object;

FIG. 78 is a side view of lenses forming the optical system;

FIG. 79 is a graphic representation showing an irradiance distributionon an object;

FIG. 80 is a graphic representation showing an irradiance distributionon a photosensitive material;

FIG. 81 is a schematic side view of an illumination apparatus accordingto the present invention;

FIG. 82 is a graphic representation showing an irradiance distributionon a photosensitive material;

FIG. 83 is a graphic representation showing a vignetting factor of aprojection lens; and

FIG. 84 is a graphic representation showing an irradiance distributionon a photosensitive material.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 8, a light source LS is located on the optical axis Z,and, when the light ray b₁ emitted from the center LS₀ of the lightsource LS enters into the entrance pupil A of a lens L at the entranceheight h, the light ray B₁ advances through the lens L and emerges fromthe exit pupil B, to reach the object P at the height H.

Similarly, a light ray entering into the entrance pupil at a height h+Δhreaches the object at a height H+ΔH. In this case, assuming that lightintensity is not lost during the light transmission through the lens,the radiant flux transmitted through the area ΔS₁ between a circle ofradius h and a circle of radius h+Δh reaches the area ΔS₂ between thecircle of radius H and that of radius H+ΔH. These areas ΔS₁ and ΔS₂ arerepresented as follows:

    ΔS.sub.1 =π{(h+Δh).sup.2 -h.sup.2 }         (4)

    ΔS.sub.2 =π{(H+ΔH).sup.2 -H.sup.2 }         (5)

Assuming that the irradiance at the incident height h at the entrancepupil A is defined as e, the irradiance E at the illumination height Hon the object P can be expressed as ##EQU3##

Then, assuming that ΔH is brought infinitely close to zero, thefollowing formulae are obtained: ##EQU4## The formula (6) then can beexpressed as follows:

    E=e·f(H)                                          (9)

where f(H)=(dh/dH)(h/H).

In order to increase the irradiance in the peripheral area of theobject, the optical system according to the present invention isdesigned to so as to satisfy the following formula:

    f(0)≦f(H)                                           (9')

In the case where the irradiance e in the entrance pupil A can beregarded as constant independent of the incident height h, in otherwords, in the case where the irradiance distribution in the entrancepupil A is uniform, the aforementioned function f(H) represents therelative irradiance on the object P in connection with the irradiance e.

The relative irradiance at the illumination height H=0 on the object Pis represented by the function f(0), whereas the relative irradiance atthe illumination height H≠0 thereon is represented by the function f(H).

By the way, in the paraxial region the illumination height H can beexpressed as follows:

    H=-{(a'-f)/fa'}b'h                                         (10)

then, the function f(0) can be expressed as follows:

    f(0)=[fa'/{(a'-f)b'}].sup.2                                (11)

where a' is the distance between the light source and the primaryprincipal point, f is the focal length, and b' is the distance betweenthe real image of the light source and the object.

FIRST EMBODIMENT

Referring to FIG. 9, which shows a schematic view of the illuminationapparatus according to the present invention, the illumination apparatuscomprises a light source 1, an ellipsoidal mirror 2 provided withrespect to the light source, an optical system 3, e.g. formed into afly's eye configuration, a diffusing plate 4, an original 5 to bereproduced placed immediately behind the diffusing plate, a projectionlens 6 and a photosensitive material 7, in order. The light source 1 isa mercury lamp, with respect to which the ellipsoidal mirror 2 isprovided. The ellipsoidal mirror is designed that the exit terminalthereof is 170 mm in radius. The optical system 3 is placed 500 mm awayfrom the exit terminal of the light source. Light reflected by themarginal end of the mirror 2 is at an angle of 18.8 degrees relative tothe optical axis, to be received by the optical system 3. Light emergedfrom the optical system 3 impinges upon the diffusing plate 4, by whichthe light is well diffused suitable for uniform illumination of theoriginal. The diffusing plate 4 is placed 1000 mm away from the exitterminal of the optical system 3. The original 5, e.g. a transparency,is placed immediately behind the diffusing plate. The projection lens 6is designed so that the focal length thereof is 600 mm and it is placed1200 mm away from the original 5. The photosensitive material 7 isplaced 1200 mm away from the exit surface of the projection lens. Inthis case, the entire area of an original having a 900 mm diagonal isilluminated, and the image illuminated is projected on thephotosensitive material at 1:1 magnification.

As mentioned above, the optical system 3 is formed into a fly's eyeconfiguration, wherein a plurality of similar optical systems arealigned two-dimensionally. In the embodiments shown hereinafter, onlyone of such optical system is illustrated.

Hereinafter described are examples of the optical system 3 to beemployed in the illumination apparatus shown in FIG. 9. In the followingexamples, the respective optical elements shown in FIG. 8 are designedas follows:

Focal length of the lens L (i.e. optical system 3 in FIG. 9) is f=1.0;

The distance between the light source LS and the optical system L (i.e.optical system 3 in FIG. 9) is a'=50; and

Size of the light source LS is 2a'tan ω.

In the case where any surface is aspherical, such aspherical surfacewill be defined with both the Z-coordinate corresponding to the opticalaxis and the Y-coordinate corresponding to the height from the opticalaxis, and the value of the Z-coordinate will be represented by thefollowing formula:

    Z=CY.sup.2 /[+{1-(K+1)C.sup.2 Y.sub.2 }.sup.1/2 ]+A.sub.1 Y.sup.4 +A.sub.2 Y.sup.6 +A.sub.3 Y.sup.8 +A.sub.4 Y.sup.10                (12)

where C=1/r (r is a radius of curvature); K is a conic constant; and A₁,A₂, A₃ and A₄ are aspheric constants.

FIRST EXAMPLE

Referring to FIG. 10, which shows a side view of the lenses forming theoptical system 3 of this example, the optical system comprises twooptical units including two lenses L₁ and L₂, wherein the second surfacer₂ thereof is aspherical. The lens data of this optical system are shownin Table 2.

                  TABLE 2                                                         ______________________________________                                        r                  d      n                                                   ______________________________________                                        1        1.2713        0.467  1.55649                                         2       -0.8983        0.249                                                  3        1.4294        1.526  1.52216                                         4       -1.4859                                                               ______________________________________                                    

The conic constant and aspheric constants of the second surface r₂ areshown in Table 3.

                  TABLE 3                                                         ______________________________________                                        K             A.sub.1                                                                              A.sub.2    A.sub.3                                                                            A.sub.4                                  ______________________________________                                        2     -1.409      0.630  0.044    0.112                                                                              0.086                                  ______________________________________                                    

In this example, the lens is so designed that the effective diameter ofthe entrance pupil A is 1.24, and that the effective view angle at thecenter of the entrance pupil A is 37.6 degrees.

FIGS. 11-(A) through 11-(C) are graphic representations showing theirradiance distribution on the object, which irradiance distribution iseffected by the light rays starting from points LS₀, LS₁ and LS₂ of thelight source, respectively. The point LS₀ corresponds to that on theoptical axis, the point LS₁ corresponds to that at the height of 70percent of the radius of the light source, and the point LS₂ correspondsto that at the upper end of the light source. In these Figures, thehorizontal axis represents the height from the optical axis on theobject, and the vertical axis represents the relative irradiance (%)when the irradiance at the center of the object is regarded as 100 (%).

It will be understood from these Figures that the irradiance on theobject increases gradually from the center toward the peripheral area.The peripheral irradiance becomes more than 150 percent in the casewhere the light rays starting from the point LS₀ irradiates the object(FIG. 11-(A)).

This example may be especially advantageous, since the refractive indexis relatively small, hence common optical glass can be used.

SECOND EXAMPLE Referring to FIG. 12, which shows a side view of thelenses forming the optical system 3 of this example, the optical systemcomprises three optical units including three lenses L₁, L₂ and L₃. Allthe surfaces thereof are spherical, and the lens data are listed inTable 4.

                  TABLE 4                                                         ______________________________________                                        r                  d      n                                                   ______________________________________                                        1       12.8443        0.599  1.64294                                         2       -1.5549        0.248                                                  3       1.1351         0.338  1.83139                                         4       -2.8552        0.301                                                  5       -1.2607        0.631  1.73621                                         6       -0.7708                                                               where the effective diameter of the lens is 1.2;                              and the effective view angle: 2ω = 43.6 degrees.                        ______________________________________                                    

FIGS. 13-(A) through 13-(C) are graphic representations showingirradiance distribution on the object, which irradiance distribution iseffected by the light rays from the points LS₀, LS₁ and LS₂ of the lightsource, respectively.

It will be understood from these Figures that the irradiance on theobject increases gradually from the center to the peripheral area.

This example may be particularly advantageous, since the effective viewangle can be relatively wide, although the optical system comprisesthree spherical lenses.

THIRD EXAMPLE

Referring to FIG. 14, which shows a side view of forming the opticalsystem 3 of this example, the optical system comprises two optical unitsincluding two lenses L₁ and L₂. All the surfaces thereof are spherical,and the lens data are listed in Table 5.

                  TABLE 5                                                         ______________________________________                                        r                  d      n                                                   ______________________________________                                        1       5.8058         0.702  1.94359                                         2       -1.5459        0.278                                                  3       0.8281         1.256  1.49028                                         4       -0.7142                                                               where the effective diameter of the lens is 1.06;                             and the effective view angle: 2ω = 27.0 degrees.                        ______________________________________                                    

FIGS. 15-(A) through 15-(C) are graphic representations showingirradiance distribution on the object, which irradiance distribution iseffected by the light rays from the points LS₀, LS₁ and LS₂ of the lightsource, respectively.

It will be understood from these Figures that the irradiance on theobject increases gradually from the center to the peripheral area. Thisexample may be particularly advantageous, since the optical systemcomprises only two spherical lenses, hence the manufacturing costs canbe decreased.

FOURTH EXAMPLE

Referring to FIG. 16, which shows a side view of the lenses forming theoptical system the optical system comprises four optical units and fourlenses L₁ to L₄. All the surfaces thereof are spherical, and the lensdata are listed in Table 6.

                  TABLE 6                                                         ______________________________________                                        r                  d       n                                                  ______________________________________                                        1       1.2970         0.3643  1.67490                                        2       -2.1677        0.1079                                                 3       -9.6551        0.2889  1.70011                                        4       -1.7124        0.1473                                                 5       0.8925         0.3064  1.66258                                        6       1.2785         0.1641                                                 7       -1.8578        0.3579  1.68473                                        8       -0.5743                                                               where the effective diameter of the lens is 1.04;                             and the effective view angle: 2ω = 40/2 degrees.                        ______________________________________                                    

FIGS. 17-(A) through 17-(B) are graphic representations showingirradiance distribution on the object, which irradiance distribution iseffected by the light rays from the points LS₀, LS₁ and LS₂ of the lightsource, respectively.

It will be understood from these Figures that the irradiance increasesgradually from the center to the peripheral area. This example may beparticularly advantageous, since all the lenses employed have lowrefractive indexes, and hence common optical glass can be used.

FIFTH EXAMPLE

Referring to FIG. 18, which shows a side view of the lenses forming theoptical system 3 of this example, the optical system comprises twooptical units including two lenses L₁ and L₂. The second and thirdsurfaces thereof are aspherical, and the lens data are listed in Tables7 and 8.

                  TABLE 7                                                         ______________________________________                                        r                  d       n                                                  ______________________________________                                        1       0.9371         0.547   1.47653                                        2       -1.0495        0.327                                                  3       0.8904         1.079   1.50661                                        4       -0.9141                                                               ______________________________________                                    

                  TABLE 8                                                         ______________________________________                                        K            A.sub.1                                                                              A.sub.2   A.sub.3                                                                             A.sub.4                                   ______________________________________                                        2     -15.133    0.271  0.555   0.522 2.048                                   3     -1.036     0.047  -1.756  -0.619                                                                              -1.637                                  where the effective diameter of the lens is 1.12;                             and the effective view angle: 2ω = 43.6 degrees.                        ______________________________________                                    

FIGS. 19-(A) through 19-(C) are graphic representations showing theirradiance distribution on the object, which irradiance distribution iseffected by the light rays from the points LS₀, LS₁ and LS₂ of the lightsource, respectively.

It will be understood from these Figures that irradiance on the objectincreases gradually from the center to the peripheral area. This examplemay be particularly advantageous, since the optical system has a wideview angle, although it comprises only two lenses.

SIXTH EXAMPLE

Referring to FIG. 20, which shows a side view of the lens forming theoptical system 3 of this example, the optical system comprises a singleoptical unit including a single lens L₁. All the surfaces thereof areaspherical, and the lens data are listed in Tables 9 and 10.

                  TABLE 9                                                         ______________________________________                                        r                  d       n                                                  ______________________________________                                        1       0.5770         2.124   1.77585                                        2       -1.3693                                                               ______________________________________                                    

                  TABLE 10                                                        ______________________________________                                        K           A.sub.1 A.sub.2   A.sub.3                                                                             A.sub.4                                   ______________________________________                                        1     -1.629    -0.010  -0.615  -0.843                                                                              -1.011                                  2     0.582     0.0     0.016   -0.100                                                                              -0.219                                  where the effective diameter of the lens is 1.02;                             the effective view angle: 2ω = 39.6 degrees;                            and the effective illumination height: 2H = 80 in diameter.                   ______________________________________                                    

FIGS. 21-(A) through 21-(C) are graphic representations showing theirradiance distribution on the object, which irradiance distribution iseffected by the light rays from the points LS₀, LS₁ and LS₂ of the lightsource, respectively.

It will be understood from these Figures that the irradiance on theobject increases gradually from the center to the peripheral area. Thisexample may be particularly advantageous, since the optical systemcomprises only a single lens, and the aspherical surfaces can bemanufactured through molding. This is practically advantageous for massproduction thereof, since there is no need to adjust the distancebetween the surfaces.

SECOND EMBODIMENT

According to another feature of the present invention, the opticalsystem 3 employed in the illumination apparatus shown in FIG. 9comprises three optical units including three lenses, the first opticalunit comprising a single positive lens having a convex rear surface, thesecond optical unit comprising a single positive lens having a convexfront surface, and the third optical unit comprising a single eitherpositive or negative lens and having a convex rear surface, the opticalsystem satisfying the following formulae:

    ______________________________________                                        -0.3f < f.sub.F < 0.3f                                                                             (13)                                                     -0.4 < (1 - n.sub.5)f/r.sub.6                                                                      (14)                                                     -0.6f < f.sub.B < 0.1f                                                                             (15)                                                     0.04 < (1 - n.sub.1)f/r.sub.2 < 0.8                                                                (16)                                                     (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 < 0                                                  (17)                                                     ______________________________________                                    

where f is the synthesized focal point of the optical system as a whole;f_(F) is the distance between the front surface of the first opticalunit and the primary focal point of the optical system; f_(B) is thedistance between the rear surface of the third optical unit and thesecondary focal point of the optical system; n₁, n₃ and n₅ arerespectively the refractive index of the first, second and third opticalunits; r₂ and r₄ are respectively the curvature of radius of the rearsurfaces of the first and second optical unit; and r₅ and r₆ arerespectively the curvature of radius of the front and rear surfaces ofthe third optical unit.

Referring to FIGS. 8 and 22 through 24, the optical system in thisembodiment comprises three optical units each of which comprises asingle lens. Both the distance a between the light source LS and thelens L and the distance b between the lens L and the object P aredesigned to be sufficiently large in comparison with the synthesizedfocal length f of the lenses L₁, L₂ and L₃. The optical system isdesigned so that the entrance pupil A is located in the vicinity of thefront surface of the first lens L₁.

The optical system according to this embodiment is designed to satisfythe formula (13);

    0.3f<f.sub.F <0.3f                                         (13)

Both the front surface of the first lens and the synthesized focal pointof the optical system are relatively close to each other, andaccordingly the object surface P will be conjugate to the front surfaceof the first lens, whereby the incident rays forming an angle relativeto the optical axis will effectively reach the object surface P, asshown in FIG. 24.

The optical system according to this embodiment is designed to satisfythe formula (14):

    0.4<(1-n.sub.5)f/r.sub.6                                   (14)

This formula (14) defines the refracting power of the surface r₆ (i.e.the rear surface of the third lens), by which the exit angle θ of therays Q₁ incident to the optical system at the incident height h iscontrolled not to be excessively large.

As shown in FIG. 23, the incident rays formed into parallel rays arerefracted by the lenses L₁ and L₂, wherein the ray entering at a largeincident height is subject to large refraction due to sphericalaberration. The intersection I₁ where the marginal rays Q₁ intersect theoptical axis Z will then be located before the intersection I₂ where theparaxial rays Q₂ intersect the optical axis.

On the other hand, as conditioned by the formula (15), the surface r₆(i.e. the rear surface of the third lens) is located behind theintersections I₁ and I₂ and has a large refracting power as defined bythe formula (14). The refracting power of the surface r₆ will notsufficiently act on the marginal rays Q₁, and the surface r₆ will rathereffect the divergence on the paraxial rays Q₂ which enters at lowincident height and intersect the optical axis behind the center ofcurvature C₆. Consequently, the optical system minimizes the exit angleθ of a marginal ray which enters at a relatively high incident height h,so that the peripheral irradiance on the object is not undesirablyreduced.

The optical system according to the embodiment is further designed tosatisfy the formula (15):

    -0.6f<f.sub.B <0.1f                                        (15)

This formula denotes that the back focal length should be designed topreferably be negative, although it may be designed to be slightlypositive.

The optical system has a sufficient length to the extent that the raysstarting out from a point away from the optical axis will not bevignetted, wherein the surface r₆ (i.e. the rear surface of the thirdlens) is located behind the intersections I₁ and I₂, and the back focallength f_(B) is defined within the range conditioned by the formula(15).

Furthermore, the optical system of this embodiment is designed tosatisfy the formula (16):

    0.04<(1-n.sub.1)f/r.sub.2 <0.8                             (16)

This formula defines the refracting power of the surface r₂ (i.e. therear surface of the first lens), by which the function of the surface r₆conditioned by the formula (14) can be fulfilled effectively.

In the case where the refracting power is less than the lowest value ofthe formula (16), the spherical aberration is small, and hence thefunction of the surface r₆ will not be fulfilled sufficiently. On theother hand, in the case where the refracting power is greater than thehighest value of the formula (16), the incident height h of the ray Q₄starting from the lower end of the light source and entering the surfacer₆ will be excessively high, and hence the exit angle θ the ray emergingtherefrom will be excessively small, accordingly the ray cannot reachthe periphery of the object.

The optical system of this embodiment is further designed to satisfy theformula (17): ##EQU5## This formula requires that the sum of both therefracting power of the surface r₄ and that of the surface r₅ isnegative.

The air lens formed between the surfaces r₄ and r₅ has a divergingfunction, by which the ray Q₄ emitted from the lower end of the lightsource and emerging from the surface r₆ is raised upward to obtain theexit angle θ.

Hereinafter described are examples of the optical system conditioned bythe formulae (13) through (17). In the following examples, the opticalsystem L (i.e. optical system in FIG. 9) is placed a=50 away from thelight source having the radius y=15, and the object P is placed b=100away from the rear surface of the optical system.

FIRST EXAMPLE

Referring to FIG. 22, which shows a side view of the optical system 3 ofthis example, the optical system comprises three optical units includingthree lenses L₁ through L₃, wherein the optical system satisfies thefollowing formulae:

    ______________________________________                                        f.sub.F = 0.24         (18)                                                   (1 - n.sub.5 f/r.sub.6 = 1.59                                                                        (19)                                                   f.sub.B = -0.04        (20)                                                   (1 - n.sub.1)f/r.sub.2 = 0.28                                                                        (21)                                                   (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1/r.sub.5 = -1.08                                                 (22)                                                   ______________________________________                                    

The lens data of this optical system are shown in Table 11.

                  TABLE 11                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       4.228           0.149  1.72                                           2       -2.587          0.298                                                 3       0.755           0.547  1.72                                           4       -2.981          0.162                                                 5       -0.607          0.457  1.8                                            6       -0.503                                                                where the synthesized focal length: f = 1;                                    the effective aperture = 1; and                                               the radius of the light source: y = 15.                                       ______________________________________                                    

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) have intermediate values.

FIG. 25 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±2 percent.

SECOND EXAMPLE

Referring to FIG. 26, which shows a side view of the lenses forming theoptical system 3 of this example, the optical system comprises threeoptical units including three lenses L₁ through L₃, wherein the opticalsystem satisfies the following formulae:

    ______________________________________                                        f.sub.F = -0.12        (23)                                                   (1 - n.sub.5)f/r.sub.6 = 0.43                                                                        (24)                                                   F.sub.B = -0.41        (25)                                                   (1 - n.sub.1)f/r.sub.2 = 0.77                                                                        (26)                                                   (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.28                                                (27)                                                   ______________________________________                                    

The lens data of this optical system are shown in Table 12.

                  TABLE 12                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       ∞         0.414  1.73                                           2       -0.942          0.578                                                 3       1.021           0.457  1.68                                           4       -1.804          0.127                                                 5       -0.832          0.654  1.55                                           6       -1.276                                                                where the synthesized focal length: f = 1;                                    the effective aperture = 1; and                                               the radius of the light source: y = 10.                                       ______________________________________                                    

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 27 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±4 percent.

THIRD EXAMPLE

Referring to FIG. 28, which shows a side view of the optical system 3 ofthis example, the optical system comprises three optical units includingthree lenses L₁ through L₃, wherein the optical system satisfies thefollowing formulae:

    ______________________________________                                        f.sub.F = 0.13         (28)                                                   (1 - n.sub.5)f/r.sub.6 = 1.25                                                                        (29)                                                   f.sub.B = 0.05         (30)                                                   (1 - n.sub.1)f/r.sub.2 = 0.07                                                                        (31)                                                   (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.22                                                (32)                                                   ______________________________________                                    

The lens data of this optical system are shown in Table 13.

                  TABLE 13                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1      6.604            0.152  1.72                                           2      -10.010          0.135                                                 3      1.242            0.522  1.72                                           4      -1.017           0.311                                                 5      -0.857           0.576  1.80                                           6      -0.642                                                                 where the synthesized focal length: f = 1;                                    the effective aperture = 1; and                                               the radius of the light source: y = 15.                                       ______________________________________                                    

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 29 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±3 percent.

FOURTH EXAMPLE

Referring to FIG. 30, which shows a side view of the optical system 3 ofthis example, the optical system comprises three optical units includingthree lenses L₁ through L₃, wherein the optical system satisfies thefollowing formulae:

    ______________________________________                                        f.sub.F = 0.17             (33)                                               (1 - n.sub.5)f/r.sub.6 = 1.60                                                                            (34)                                               f.sub.B = -0.22            (35)                                               (1 - n.sub.1)f/r.sub.2 = 0.05                                                                            (36)                                               (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.65                                                    (37)                                               ______________________________________                                    

The lens data of this optical system are shown in Table 14.

                  TABLE 14                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1        1.903          0.152  1.72                                           2       -14.445         0.176                                                 3        1.082          0.519  1.72                                           4       -0.993          0.356                                                 5       -0.581          0.384  1.80                                           6       -0.501                                                                ______________________________________                                    

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 31 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±2 percent.

FIFTH EXAMPLE

Referring to FIG. 32, which shows a side view of the optical system 3 ofthis example, the optical system comprises three optical units includingthree lenses L₁ through L₃, wherein the optical system satisfies thefollowing formulae:

    ______________________________________                                        f.sub.F = 0.18             (38)                                               (1 - n.sub.5)f/r.sub.6 = 0.51                                                                            (39)                                               f.sub.B = -0.57            (40)                                               (1 - n.sub.1)f/r.sub.2 = 0.50                                                                            (41)                                               (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.47                                                    (42)                                               ______________________________________                                    

The lens data of this optical system are shown in Table 15.

                  TABLE 15                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       ∞         0.232  1.70                                           2       -1.403          0.689                                                 3        0.539          0.451  1.70                                           4        2.855          0.265                                                 5       -2.327          0.619  1.51                                           6       -1.000                                                                ______________________________________                                         wher the synthesized focal length: f = 1; the effective aperture = 1; and     the radius of the light source: y = 10.                                  

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 33 shows the irradiance distribution o the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±4 percent.

SIXTH EXAMPLE

Referring to FIG. 34, which shows a side view of the optical system 3 ofthis example, the optical system comprises three optical units includingthree lenses L₁ through L₃, wherein the optical system satisfies thefollowing formulae:

    ______________________________________                                        f.sub.F = 0.14             (43)                                               (1 - n.sub.5)f/r.sub.6 = 1.35                                                                            (44)                                               f.sub.B = -0.15            (45)                                               (1 - n.sub.1)f/r.sub.2 = 0.40                                                                            (46)                                               (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.93                                                    (47)                                               ______________________________________                                    

The lens data of this optical system are shown in Table 16.

                  TABLE 16                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1        4.251          0.150  1.72                                           2       -1.780          0.350                                                 3        0.760          0.484  1.72                                           4       -2.997          0.163                                                 5       -0.626          0.480  1.73                                           6       -0.540                                                                ______________________________________                                         where the synthesized focal length: f = 1; the effective aperture = 1; an     the radius of the light source: y = 15.                                  

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 35 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance in the peripheral area of the object is increased about 20percent.

SEVENTH EXAMPLE

Referring to FIG. 36, which shows a side view of comprises three opticalunits including three lenses L₁ through L₃, wherein the optical systemsatisfies the following formulae:

    ______________________________________                                        f.sub.f = -0.04            (48)                                               (1 - n.sub.5)f/r.sub.6 = 0.90                                                                            (49)                                               f.sub.B = -0.24            (50)                                               (1 - n.sub.1)f/r.sub.2 = 0.25                                                                            (51)                                               (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.45                                                    (52)                                               ______________________________________                                    

The lens data of this optical system are shown in Table 17.

                  TABLE 17                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1        1.307          0.312  1.51                                           2       -2.01           0.181                                                 3        0.603          0.338  1.51                                           4        3.012          0.422                                                 5       -1.81           0.302  1.51                                           6       -0.568                                                                ______________________________________                                         where the synthesized focal length: f = 1; the effective aperature = 1;       and the radius of the light source: y = 14.                              

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 37 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±5 percent.

EIGHTH EXAMPLE

Referring to FIG. 38, which shows a side view of the optical system 3 ofthis example, the optical system comprises three optical units includingthree lenses L₁ through L₃, wherein the optical system satisfies thefollowing formulae:

    ______________________________________                                        f.sub.F = -0.18            (53)                                               (1 - n.sub.5)f/r.sub.6 = 0.53                                                                            (54)                                               f.sub.B = -0.08            (55)                                               (1 - n.sub.1)f/r.sub.2 = 0.39                                                                            (56)                                               (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 = -0.08                                                    (57)                                               ______________________________________                                    

The lens data of this optical system are shown in Table 18.

                  TABLE 18                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       3.502           0.232  1.671                                          2       -1.700          0.269                                                 3       1.028           0.430  1.671                                          4       4.161           0.276                                                 5       6.126           0.481  1.51                                           6       -0.961                                                                ______________________________________                                         where the synthesized focal length: f = 1; the effective aperature = 1;       and the radius of the light source: y = 14.                              

In the example, the optical system is designed so that the conditionsdefined by the formulae (13) through (17) are satisfied.

FIG. 39 shows the irradiance distribution on the object effected by theoptical system of this example, from which it can be understood that theirradiance distribution on the object is within the range of ±5 percent.

According to the embodiment conditioned by the formulae (13) through(17), the optical system enables the irradiance within the range of 80to 90 in diameter on the object to be approximately uniform oreffectively increased in the peripheral area thereof, which rangecorresponds to the exit angle of 22 to 27 degrees.

In comparison with a conventional illumination apparatus, by whichuniform irradiation distribution to the extent of ±5 percent on theobject can be effected within only about 10 degrees of the exit angle,the distance between the optical system and the object can be reduced upto half to one-third when the same area is illuminated withapproximately the same irradiance distribution.

THIRD EMBODIMENT

According to a further feature of the present invention, the opticalsystem 3 employed in the illumination apparatus shown in FIG. 9comprises four optical units including four lenses, the first opticalunit comprising a single positive lens and having a convex rear surface,the second optical unit comprising a single either positive or negativelens and having a convex rear surface, the third optical unit comprisinga single positive lens and having a convex front surface, the fourthoptical unit comprising a single positive lens and having a convex rearsurface, the synthesized focal length of both the first and secondlenses being positive, the optical system satisfying the followingformulae:

    0.8≦{(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f   (58)

    0.75f≦f.sub.3.4 ≦1.52f                       (59)

where f is a synthesized focal length of the optical system as a whole;f₃.4 is a synthesized focal length of both the third and fourth lenses;n₅ and n₇ are respectively the refractive index of the third and fourthlens; and r₅ and r₈ are respectively the radius of curvature of thethird and fourth lens.

In this embodiment the first and second optical units L₁ and L₂ performa part of functions of a condenser lens, since the synthesized focallength of these optical units is positive. The first optical unitcomprises a single positive lens and has a convex rear surface and thesecond optical unit comprises a single either positive or negative lensand has a convex rear surface. These optical units will accordinglycause both the large spherical aberration and coma.

Because of the spherical aberration the intersection of both themarginal rays Q₁ and the optical axis Z will be located before theintersection of both the paraxial rays Q₂ and the optical axis. Becauseof the coma the exit angle θ of the marginal ray Q₃ is controlled not beexcessively large.

On the other hand, the third optical unit L₃ comprises a single positivelens and has a convex front surface which functions as a condenser lens,whereas the fourth optical comprises a single positive lens and has aconvex rear surface. These optical units in combination with each otherfunction as a field lens and enable the peripheral irradiation of theobject to be uniform or increased.

As can be seen in FIG. 41, the rear surface r₈ of the fourth lens L₄ islocated behind the image points I₁ and I₂. The refracting power of thesurface r₈ will not effectively act on the marginal rays Q₁, which enterat large incident height and intersects the optical axis at the pointI₁, the diverging function will rather act on the paraxial rays Q₂,which enter at a small incident height and intersects the optical axisat the point I₂. In other words, the lenses L₃ and L₄ control the exitangle θ of rays entering at a relatively large incident height, to avoidthe irradiance reduction in the peripheral area of the object.

In order to enable the optical system to control the exit angle and toavoid the irradiance reduction in the peripheral area of the object, itwill be most effective that both the front surface of the third lens andthe rear surface of the fourth lens have high refracting power. For thisreason, the following condition is given:

    0.8<{(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f          (58)

The formula (58) denotes that the irradiance reduction cannot becorrected when the right-side of the formula is smaller than 0.8.

The lenses L₃ and L₄ also satisfy the following condition:

    0.75f≦f.sub.3.4 ≦1.52f                       (59)

The formula (59) denotes that the lenses L₃ and L₄ are designed to havethe function of a field lens and to avoid the eclipse caused byvignetting. When the value of the synthesized focal length f₃.4 issmaller than 0.75f, the refracting power acting on the marginal rays Q₃,will be excessively strong, and then the exit angle will becomeexcessively small, accordingly an effective illumination area on theobject will become small.

On the contrary, when the value of the synthesized focal length f₃.4 islarger than 1.52f, an image formed in the conjugate plane of theentrance pupil will become small, since the magnification is in inverseproportion to the value f₃.4 due to the conjugate relationship betweenthe entrance pupil and the image plane. Further, the refracting power ofthe lenses L₃ and L₄ will become small, and it will then be impossibleto minimize, independent of the size of the light source, the exit angleof the rays entering at a large incident height, and consequently aremarkable irradiance reduction will be caused in the peripheral area ofthe object.

In the light of this, the formula (59) defines a preferable range of thesynthesized focal length to satisfactorily achieve the correction of theirradiance reduction in the peripheral area of the object.

Hereinafter described are examples of the optical system conditioned bythe formulae (58) and (59). In the following examples, the opticalsystem L (i.e. optical system 3 in FIG. 9) is designed so that thediameter of the light source=20 (maximum incident angle ω_(max) =11.3degrees); the distance between the light source and the entrancepupil=50; the distance between the rear surface of the fourth lens andthe object=100; the diameter of the object=80 (maximum exit angleθ_(max) =21.8 degrees); the effective diameter of respective lenses=1.0;and the synthesized focal length of the optical system as a whole=1.0.The optical system is further designed so that the entrance pupil A isplaced at the front surface of the first lens L₁, and that the image ofthe entrance pupil is imaged on the object.

FIRST EXAMPLE

Referring to FIG. 40, which shows a side view of the optical system 3 ofthis example, the optical system comprises four optical units includingfour lenses L₁ through L₄, wherein the optical system satisfies thefollowing formulae:

    {(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f=1.54         (64)

    f.sub.3.4 =1.12                                            (65)

The lens data of this optical system are shown in Table 19.

                  TABLE 19                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       157.254       0.302  1.70                                             2       -3.277        0.201                                                   3        6.700        0.297  1.70                                             4       -1.409        0.494                                                   5        0.654        0.225  1.70                                             6        2.551        0.273                                                   7       -3.100        0.597  1.487712                                         8       -1.038                                                                ______________________________________                                    

FIG. 43 shows an irradiance distribution on the object, from which itwill be apparent that the irradiance is increases gradually toward thethe peripheral area.

SECOND EXAMPLE

Referring to FIG. 44, which shows a side view of the optical system 3 ofthis example, the optical system comprises four optical units includingfour lenses L₁ through L₄, wherein the optical system satisfies thefollowing formulae:

    {(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f=1.47         (66)

    f.sub.3.4 32 1.33                                          (67)

The lens data of this optical system are shown in Table 20.

                  TABLE 20                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       -9.118        0.320  1.802062                                         2       -1.791        0.066                                                   3        10.968       0.164  1.642258                                         4       -2.555        0.542                                                   5        0.529        0.307  1.625456                                         6        0.759        0.320                                                   7        3.723        0.376  1.493998                                         8       -1.693                                                                ______________________________________                                    

FIG. 45 shows an irradiance distribution on the object. In this example,the optical system is designed so that the maximum illuminationheight=97.6 in diameter (maximum exit angle: θ_(max) =26 degrees), andthat the irradiance reduction in the intermediate area of the object iscontrolled to increase the irradiance in the peripheral area of theobject.

THIRD EXAMPLE

Referring to FIG. 46, which shows a side view of the optical system 3 ofthis example, the optical system comprises four optical units includingfour lenses L₁ through L₄, wherein the optical system satisfies thefollowing formulae:

    {(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f=3.05         (68) )

    f.sub.3.4 =0.7515                                          (69)

The lens data of this optical system are shown in Table 21.

                  TABLE 21                                                        ______________________________________                                        r                 d       n                                                   ______________________________________                                        1        1.220        0.626   1.797216                                        2       -2.452        0.203                                                   3       -1.064        0.039   1.654937                                        4       -7.405         0.0009                                                 5        0.561        0.249   1.810782                                        6        1.889        0.203                                                   7       -0.894        0.342   1.800000                                        8       -0.500                                                                ______________________________________                                    

FIG. 47 shows an irradiance distribution effected on the object by thisexample. This example is the case where the synthesized focal lengthf₃.4 is of the minimum value.

FOURTH EXAMPLE

Referring to FIG. 48, which shows a side view of the optical system 3 ofthis example, the optical system comprises four optical units includingfour lenses L₁ through L₄, wherein the optical system satisfies thefollowing formulae:

    {(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f=1.00         (70)

    f.sub.3.4 =1.508                                           (71)

The lens data of this optical system are shown in Table 22.

                  TABLE 22                                                        ______________________________________                                        r                  d      n                                                   ______________________________________                                        1       -5.889         1.285  1.606160                                        2       -2.294         0.007                                                  3       -8.658         0.101  1.728480                                        4       -1.503         0.638                                                  5        0.614         0.357  1.596283                                        6        1.058         0.557                                                  7        1.846         0.312  1.470449                                        8       -18.716                                                               ______________________________________                                    

FIG. 49 shows an irradiance distribution effected on the object byoptical system. This example is the case where the synthesized focallength f₃.4 is of the minimum value.

FIFTH EXAMPLE

Referring to FIG. 50, which shows a side view of the optical system 3 ofthis example, the optical system comprises four optical units includingfour lenses L₁ through L₄, wherein the optical system satisfies thefollowing formulae:

    {(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f=0.805        (72)

    f.sub.3.4 =1.242                                           (73)

The lens data of this optical system are shown in Table 23.

                  TABLE 23                                                        ______________________________________                                        r                 d       n                                                   ______________________________________                                        1      -26.528         0.0696 1.689773                                        2      -2.844          0.0768                                                 3      -3.473         0.507   1.771712                                        4      -1.155         0.527                                                   5       0.819         0.174   1.499915                                        6       4.817         0.350                                                   7       1.743         0.576   1.470449                                        8      -2.485                                                                 ______________________________________                                    

FIG. 51 shows an irradiance distribution effected on the object by thisexample. This example is the case where the sum of both the refractingpowers of the front surface of the third lens and the rear surface ofthe fourth lens is of the minimum value.

SIXTH EXAMPLE

Referring to FIG. 52, which shows a side view of the optical system 3 ofthis example, the optical system comprises four optical units includingfour lenses L₁ through L₄, wherein the optical system satisfies thefollowing formulae:

    {(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f=1.735        (74)

    f.sub.3.4 =0.967                                           (75)

The lens data of this optical system are shown in Table 24.

                  TABLE 24                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       1.503         0.155  1.757631                                         2       -2.123        0.202                                                   3       -1.286        0.115  1.434101                                         4       -1.320        0.019                                                   5       5.000         0.230  1.680075                                         6       -3.996        0.278                                                   7       -0.818        0.339  1.800000                                         8       -0.500                                                                ______________________________________                                    

FIG. 53 shows the irradiance distribution effected on the object by thisexample, from which it will be apparent that the irradiance is more than93 percent throughout the object.

FOURTH EMBODIMENT

According to a further feature of the present invention, the opticalsystem 3 employed in the illumination apparatus shown in FIG. 9 includestwo optical units including two lenses, the first optical unitcomprising a single positive lens having a convex rear surface and thesecond optical unit comprising a single positive lens having convexfront and rear surfaces, the optical system satisfying the followingformulae:

    -3.0≦(d.sub.3 /r.sub.4)≦-0.3                 (76)

    1.0f≦f.sub.2 ≦1.55f                          (77)

where f is a synthesized focal length of the optical system as a whole;f₂ is the focal length of the second optical unit; d₃ is the thicknessof the second optical unit; and r₄ is the radius of curvature of therear surface of the second optical unit.

According to this embodiment, the incident rays entering into theoptical system are subject to the refracting power of the rear surfaceof the first lens L₁, and the larger the incident height of the enteringray, the more strongly the refracting power of the rear surface of thefirst lens acts on the same due to the spherical aberration. As shown inFIG. 55, the intersection I₁ of both the marginal rays Q₁ and theoptical axis Z accordingly is located before the intersection I₂ of boththe paraxial rays Q₂ and the optical axis.

The rear surface r₄ of the second lens L₂ locates behind theintersections I₁ and I₂ and has a strong refracting power. Therefracting power of the surface r₄ will not act on the marginal rays Q₁,and the diverging function will rather act on the paraxial rays Q₂. Theoptical system of this embodiment controls the exit angle of the raysentering at relatively large incident height, so that the irradiancereduction in the peripheral area of the object is effectively resolved.

The rear surface of the first lens L₁ effects the positive coma, whichimplies that the rear surface r₂ of the first lens L₁ is defined withinthe range where the incident height to the rear surface r₄ of the secondlens L₂ of a marginal ray Q₃ will not become excessively large, as canbe seen in FIG. 56. This is because, when the incident height to therear surface r₄ of the second lens is excessively large, the exit angleθ therefrom will, to the contrary, become excessively small due to therefracting power of the surface r₄, and the effective illumination areawill accordingly become small.

The optical system of this embodiment is designed to satisfy the formula(76):

    -3.0≦(d.sub.3 /r.sub.4)≦-0.3                 (76)

This condition defined by the formula (76) ensures that the raysrefracted by the rear surface r₄ of the first lens L₂ is not subject tothe vignetting caused by a lens barrel and does not emerge therefrom atan excessively small exit angle.

When the value of (d₃ /r₄) is smaller than -3.0, the refracting power ofthe surface r₄ will become large since the radius of curvature of thesurface r₄ is negative, and the exit angle of the marginal rays Q₁ andQ₃ will accordingly become excessively small. Consequently, theeffective illumination area of the object will become small. In thiscase, the thickness d₃ of the second lens L₂ will become relativelylarge, and the vignetting will accordingly be caused to effect loss oflight intensity.

On the other hand, when the value of (d₃ /r₄) is larger than -0.3, it isnecessary in order to improve the refracting power of the second lens L₂that the radius of curvature r₃ of the front surface thereof is small asshown by an imaginary line in FIG. 56, and that the distance d₂

between the lenses is large. The marginal ray Q₃ entering the lower endof the first lens will then impinge upon the front surface of the secondlens at a larger incident height, and the refracting power of the frontsurface of the second lens will accordingly act thereon to result in anexcessively small exit angle θ, thereby the effective illumination areaon the object will consequently become small.

The optical system of this embodiment is further designed to satisfy theformula (77):

    1.0f≦f.sub.2 ≦1.55f                          (77)

When the value of the focal length f₂ of the second lens L₂ is smallerthan 1.0f, the refracting power of the second lens will strongly act onthe marginal ray Q₃, and the exit angle thereof will accordingly becomesmall, thereby the effective illumination area will become small.

On the other hand, when the value of the focal length f₂ is larger than1.55f, the image of the entrance pupil which is placed at the conjugateposition to the object will become small, since the magnification is ininverse proportion to the value f₂ due to the conjugate relationshipbetween the entrance pupil and the object. In this case, since therefracting power of the second lens will become small, it willaccordingly be impossible that the exit angle of the rays entering atrelatively large incident height cannot be controlled to be smallindependent of the size of the light source, thereby the irradiance onthe object will be rapidly reduced particularly in the intermediate areathrough the peripheral area of the object.

Hereinafter described are examples of the optical system of thisembodiment. In the following examples, the optical system L (i.e.optical system 3 in FIG. 9) is designed so that the diameter of thelight source=17.64 (maximum incident angle: ω_(max) =10 degrees); thedistance a between the light source and the entrance pupil A=50; thedistance between the rear surface of the second lens and the object=100;the diameter of the object=90 (maximum exit angle θ_(max) =24.2degrees); the effective diameter of the lens=1.0; and the synthesizedfocal length of the optical system as a whole=1.0. The optical system isfurther designed so that the entrance pupil A is placed at the frontsurface of the first lens L₁, and that the image of the entrance pupilis imaged on the object.

FIRST EXAMPLE

Referring to FIG. 54, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    (d.sub.3 /r.sub.4)=-1.541                                  (78)

    f.sub.2 =1.526                                             (79)

The lens data of this optical system are shown in Table 25.

                  TABLE 25                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       8.067           0.2    1.95                                           2       -1.071          0.254                                                 3       1.997           1.290  1.450                                          4       -0.837                                                                ______________________________________                                    

FIG. 57 shows an irradiance distribution on the object, from which itwill be understood that it is within the range of ±4 percent. Thisexample is the case where the focal length f₂ is approximately ofmaximum value.

SECOND EXAMPLE

Referring to FIG. 58, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    (d.sub.3 /r.sub.4)=-3.0                                    (80)

    f.sub.2 =1.07                                              (81)

The lens data of this optical system are shown in Table 26.

                  TABLE 26                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       -2.975          0.296  1.95                                           2       -1.331          0.025                                                 3       0.672           1.518  1.45                                           4       -0.506                                                                ______________________________________                                    

FIG 59 shows an irradiance distribution on the object, from which itwill be understood that the it is within the range of ±4 percent. Thisexample is the case where the value of (d₃ /r₄) is of the minimum value.

THIRD EXAMPLE

Referring to FIG. 60, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    (d.sub.3 /r.sub.4)=-0.3                                    (82)

    f.sub.2 =1.207                                             (83)

The lens data of this optical system are shown in Table 27.

                  TABLE 27                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       5.879         0.534  1.925645                                         2       -1.530        0.696                                                   3       1.285         1.150  1.891828                                         4       -3.831                                                                ______________________________________                                    

FIG. 61 shows an irradiance distribution on the object, from which it isunderstood that the irradiance reduction in the intermediate area iswithin several percent, and that the peripheral irradiance is ratherincreased several percent. This example is the case where the value of(d₃ /r₄) is of maximum value.

FOURTH EXAMPLE

Referring to FIG. 62, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    (d.sub.3 /r.sub.4)=-1.525                                  (84)

    f.sub.2 =1.022                                             (85)

The lens data of this optical system are shown in Table 28.

                  TABLE 28                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       1.281         0.554  1.936256                                         2       -1.953        0.149                                                   3       2.651         1.288  1.744523                                         4       -0.845                                                                ______________________________________                                    

FIG. 63 shows an irradiance distribution on the object, from which it isunderstood that the irradiance in the peripheral area is sufficientlyincreased. This example is the case where the focal length f₂ is theshortest among the examples.

FIFTH EXAMPLE

Referring to FIG. 64, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    (d.sub.3 /r.sub.4)=-2.258                                  (86)

    f.sub.2 =1.319                                             (87)

The lens data of this optical system are shown in Table 29.

                  TABLE 29                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       -1.599        0.850  1.501881                                         2       -0.814        0.050                                                   3       0.923         1.660  1.450000                                         4       -0.735                                                                ______________________________________                                    

FIG. 65 shows an irradiance distribution on the object, from which it isunderstood that the irradiance in the peripheral area is sufficientlyincreased.

SIXTH EXAMPLE

Referring to FIG. 66, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    (d.sub.3 /r.sub.4)=-1.899                                  (88)

    f.sub.2 =1.434                                             (89)

The lens data of this optical system are shown in Table 30.

                  TABLE 30                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       1.815         0.232  1.95                                             2       -1.407        0.134                                                   3       3.855         1.375  1.469959                                         4       -0.724                                                                ______________________________________                                    

FIG. 67 shows an irradiance distribution on the object, from which it isunderstood that the irradiance reduction in the intermediate area iswithin several percent, whereas the irradiance in the peripheral area isslightly increased.

FIFTH EMBODIMENT

According to a further feature of the present invention, the opticalsystem 3 employed in the illumination apparatus shown in FIG. 9 includestwo optical units including two lenses, the first optical unitcomprising a single positive lens and having a convex rear surface thesecond optical unit comprising a single positive lens and having aconcave front surface and a convex rear surface, the optical systembeing designed to satisfy the following formulae:

    -0.68≦{(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f≦0.90 (90)

    0.67≦{(1-n.sub.3)/r.sub.4 }f                        (91)

where f is a synthesized focal length of the optical system as a whole;r₂, r₃, and r₄ are a radius of curvature of the rear surface of thefirst optical unit, of the front and rear surfaces of the second opticalunit, respectively; and n₁ and n₃ are refractive indexes of the firstand second optical units.

In this embodiment, both the distance a between the light source and thefront surface of the optical system and the distance b' between the rearsurface of the optical system and the object are sufficiently large incomparison with the synthesized focal length f. The intermediate imageof the light source is formed in the vicinity of the second lens,whereas the image of the entrance pupil A is formed on the object by thesecond lens.

This embodiment performs substantially the same functions as the fourthembodiment. For example, as shown in FIG. 69, the incident rays enteringinto the optical system are subject to the refracting power of the rearsurface of the first lens L₁, and the larger the incident height of theray entering, the more strongly the refracting power of the rear surfaceof the first lens acts on the same due to the spherical aberration. Theintersection I₁ of both marginal rays Q₁ and the optical axis Zaccordingly is located before the intersection I₂ of both the paraxialrays Q₂ and the optical axis.

The rear surface r₄ of the second lens L₂ is located behind theintersections I₁ and I₂ and has a strong refracting power. Therefracting power of the surface r₄ will not act on the marginal ray Q₁,and the diverging function will rather act on the paraxial ray Q₂. Theoptical system of this embodiment controls the exit angle of the raysentering at relatively large incident height, so that the irradiancereduction in the peripheral area of the object is effectively resolved.

The rear surface of the first lens L₁ affects the positive coma, whichimplies that the rear surface r₂ of the first lens L₁ is defined withinthe range where the incident height to the rear surface r₄ of the secondlens L₂ of a marginal ray Q₃ will not become excessively large, as canbe seen in FIG. 70. This is because, when the incident height to therear surface r₄ of the second lens is excessively large, the exit angleθ therefrom will, to the contrary, become excessively small due to therefracting power of the surface r₄, and the effective illumination areawill accordingly become small.

The optical system of this embodiment is designed to satisfy theformulae (90) and (91):

    -0.68≦{(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f≦0.90 (90)

    0.67≦{(1-n.sub.3)/r.sub.4 }f                        (91)

The formula (91) requires that the irradiance distribution on the objectbe uniform or increased in the peripheral area thereof, and that a wideillumination area be ensured. Both the sum of the refracting powers ofthe rear surface of the first lens L₁ and of the front surface of thesecond lens L₂, and the refracting power of the second lens will affectthe conjugate relationship between the entrance pupil and the object.

When the value of {(1-n₁)/r₂ +(n₃₋₁)r₃ }f is smaller than -0.68, anintermediate image at the entrance pupil will become excessively small,hence the effective illumination area will become small.

On the other hand, when the value of {(1-n.sub.)/r₂ +(n₃ -1)/r₃ }f islarger than 0.90, the refracting power of the rear surface of the secondlens will become small in order to keep the conjugate relationship. Therear surface r₄ of the second lens will not significantly affect theirradiance distribution, and accordingly, when the value of {(1-n₁)/r₂+(n₃ -1)/r₃ }f is larger than 0.90 and the value of {(1-n₃)/r₄ }f issmaller than 0.67, the irradiance reduction in the intermediate areabecomes excessively large, and further the irradiance in the peripheralarea becomes decreased.

Hereinafter described are examples of the optical system of thisembodiment. In the following examples, the optical system L (i.e.optical system 3 in FIG. 9) is designed so that the diameter of thelight source=17.64 (maximum incident angle: ω_(max) =10 degrees); thedistance a between the light source and the entrance pupil=50; thedistance between the rear surface of the optical system and theobject=100; the diameter of the object=90 (maximum exit angle θ_(max)=24.2 degrees); the effective diameter of the lens=1.0; and thesynthesized focal length of the optical system as a whole=1.0.

FIRST EXAMPLE

Referring to FIG. 68, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    {(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f=-0.011       (92)

    {(1-n.sub.3)/r.sub.4 }f=1.429                              (93)

The lens data of this optical system are shown in Table 31.

                  TABLE 31                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       1.474         1.062  1.95                                             2       -0.914        0.308                                                   3       -0.683        0.464  1.717552                                         4       -0.502                                                                ______________________________________                                    

FIG. 71 shows an irradiance distribution on the object, from which it isunderstood that irradiance reduction in the intermediate area is within3 percent, and that the irradiance in the peripheral area is effectivelyincreased. This example is a standard case among the examples.

SECOND EXAMPLE

Referring to FIG. 72, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    {(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f=0.895        (94)

    {(1-n.sub.3)/r.sub.4 }f=0.676                              (95)

The lens data of this optical system are shown in Table 32.

                  TABLE 32                                                        ______________________________________                                        r                   d      n                                                  ______________________________________                                        1       10.897          0.948  1.95                                           2       -0.991          0.388                                                 3       -7.048          0.780  1.45                                           4       -0.666                                                                ______________________________________                                    

FIG. 73 shows an irradiance distribution on the object, from which it isunderstood that irradiance reduction in the intermediate area is withinseveral percent, and that the irradiance in the peripheral area is tothe contrary increased several percent.

This example is a standard case where the value of {(1-n₁)/r₂ +(n₃-1)/r₃ }f is close to the maximum value of the conditional formula (90)and the value of {(1-n₃)/r₄ }f is close to the minimum value of theformula (91).

THIRD EXAMPLE

Referring to FIG. 74, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    {(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f=0.522        (96)

    {(1-n.sub.3)/r.sub.4 }f=0.911                              (97)

The lens data of this optical system are shown in Table 33.

                  TABLE 33                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       6.289         0.887  1.95                                             2       -0.945        0.328                                                   3       -1.141        0.703  1.551803                                         4       -0.606                                                                ______________________________________                                    

FIG. 75 shows an irradiance distribution on the object, from which it isunderstood that irradiance reduction in the intermediate area is withinseveral percent, and that the irradiance in the peripheral area issufficiently increased.

FOURTH EXAMPLE

Referring to FIG. 76, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    {(1-n.sub.1)/r.sub.2+ (n.sub.3-1)/r.sub.3 }f=-0.680        (98)

    {(1-n.sub.3)/r.sub.4 }f=1.742                              (99)

The lens data of this optical system are shown in Table 34.

                  TABLE 34                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       1.461         0.911  1.900671                                         2       -1.133        0.297                                                   3       -0.593        0.447  1.874634                                         4       -0.502                                                                ______________________________________                                    

FIG. 77 shows an irradiance distribution on the object, from which it isunderstood that irradiance reduction in the intermediate area is withinseveral percent, and that the irradiance in the peripheral area issufficiently increased.

FIFTH EXAMPLE

Referring to FIG. 78, which shows a side view of the optical system 3 ofthis example, the optical system comprises two optical units includingtwo lenses L₁ and L₂, wherein the optical system satisfies the followingformulae:

    {(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f=-0.302       (100)

    {(1-n.sub.3)/r.sub.4 }f=1.416                              (101)

The lens data of this optical system are shown in Table 35.

                  TABLE 35                                                        ______________________________________                                        r                 d      n                                                    ______________________________________                                        1       1.870         0.905  1.95                                             2       -0.991        0.320                                                   3       -0.589        0.471  1.742235                                         4       -0.524                                                                ______________________________________                                    

FIG. 79 shows an irradiance distribution on the object, from which it isunderstood that the irradiance is within ±3 percent throughout theobject.

In the aforementioned embodiments, the optical system 3 is formed into aso-called fly's eye configuration, in which a plurality of elementlenses are aligned two-dimensionally. Such fly's eye configuration isespecially advantageous for use in an illumination apparatus.

According to the preset invention, in the case where a projection lens 6is disposed behind an object to be illuminated (i.e. an original 5), asshown in FIG. 9, the irradiance distribution on a photosensitivematerial 7 will be uniform throughout the entire surface thereof despitethe cosine fourth law caused by the projection lens. The examples wherethe irradiance is gradually increased in the peripheral area of theobject may particularly be adaptable for obtaining a uniform irradianceon the photosensitive material. For instance, when the example shown inFIGS. 10 and 11-(A) through 11-(C) is employed in the optical system 3shown in FIG. 9, the irradiance distribution will be uniform on thephotosensitive material 7, which irradiance distribution is shown inFIG. 80.

MODIFIED EMBODIMENT

Referring to FIG. 81, which shows another illumination apparatusaccording to the present invention, the structure of the illuminationapparatus is basically the same as that shown in FIG. 9 except anapplication of a Fresnel lens. The Fresnel lens 81 is designed that thefocal length thereof is 1200 mm, and is disposed between the diffusingplate 4 and the original to be illuminated 5.

When the Fresnel lens 81 is placed in the manner described above, theirradiance in the peripheral area of the photosensitive material 7 willbe reduced according to the cosine third law. The application of theoptical system 3 will, however, correct the irradiance distribution onthe photosensitive material 7, and the resultant irradiance distributionthereon is shown in FIG. 82, which is obtained by employing the exampleshown in FIG. 10 in the optical system 3 shown in FIG. 81. It will beunderstood that the irradiance distribution on the photosensitivematerial is well corrected and is within ±5 percent.

The aforementioned embodiments are in the case where no vignetting iscaused. Some projection lenses may often cause the vignetting, as thefield angle θ₁ thereof increases. In this case, the irradiance on theobject to be illuminated can be expressed by the product of both cos ⁴θ₁ and the vignetting factor of the projection lens to be used.

FIG. 83 shows an example of the vignetting factor of a projection lens.In the case where the illumination apparatus shown in FIG. 81 is used,which case will cause the irradiance reduction according to the cosinethird law, the irradiance distribution on the photosensitive material 7results as shown in FIG. 84, from which the irradiance distribution iswithin ±5 percent.

While the invention has been illustrated and described as embodied inspecific forms of illumination apparatus, it is not intended to belimited to the details shown, since various modifications and structuralchanges may be made without departing in any way from the spirit of thepresent invention.

Without further analysis, the foregoing will so fully reveal the gist ofthe present invention that others can, by applying current knowledge,readily adapt it for various applications without omitting featuresthat, from the standpoint of prior art fairly constitute essentialcharacteristics of the generic or specific aspects of this invention.

What is claimed as new and desired to be protected by letters patent isset forth in the appended claims.

We claim:
 1. An optical system for use in illuminating an objectcomprising:a light source; an entrance pupil for receiving light fromthe light source; an exit pupil for passing the light received to theobject; and an optical axis which extends through the optical system tothe light source and the object respectively, wherein the relationshipamong an incident height h to the entrance pupil, an illumination heightH on the object and a changing rate (dh/dH) of the incident height andthe illumination height is defined by a function f(H):

    f(H)=(h/H)(dh/dH)

the optical system being designed so as to satisfy the following formulain the peripheral area of the object:

    f(0)≦F(H)

f(0) being represented by the formula:

    f(0)=[fa'/{(a'-f)b'}].sup.2

where a' is the distance between the light source and the primaryprincipal point of the optical system, and b' is the distance betweenthe real image of the light source and the object.
 2. An optical systemfor use in illuminating an object comprising three optical units, thefirst optical unit including a positive lens and having a convex rearsurface, the second optical unit including a positive lens and having aconvex front surface, the third optical unit including either a positiveor negative lens and having a convex rear surface, the optical systemsatisfying the following formulae:

    ______________________________________                                        -0.3f < f.sub.F < 0.3f                                                        0.4 < (1 - n.sub.5)f/r.sub.6                                                  -0.6f < f.sub.B < 0.1f                                                        0.04 < (1 - n.sub.1)f/r.sub.2 < 0.8                                           (1 - n.sub.3)/r.sub.4 + (n.sub.5 - 1)/r.sub.5 < 0                             ______________________________________                                    

where f is the synthesized focal point of the optical system; f_(F) isthe distance between the front surface of the first optical unit and theprimary focal point of the optical system; f_(B) is the distance betweenthe rear surface of the third optical unit and the secondary focal pointof the optical system; n₁, n₃ and n₅, are respectively the refractiveindex of the first, second and third optical units; r₂ and r₄ arerespectively the radius of curvature of the rear surfaces of the firstand second optical units; and r₅ and r₆ are respectively the radius ofcurvature of the front and rear surfaces of the third optical unit. 3.An optical system for use in illuminating an object comprising fouroptical units, the first optical unit including a positive lens andhaving a convex rear surface, the second optical unit including either apositive or negative lens and having a convex rear surface, the thirdoptical unit including a positive lens and having a convex frontsurface, the fourth optical unit including a positive lens and having aconvex rear surface, the synthesized focal length of both the first andsecond optical units being positive, the optical system satisfying thefollowing formulae:

    0.8≦{(n.sub.5 -1)/r.sub.5 +(1-n.sub.7)/r.sub.8 }f

    0.75f≦f.sub.3.4 ≦1.52f

where f is a synthesized focal length of the optical system; f₃.4 is asynthesized focal length of both the third and fourth optical units; n₅and n₇ are respectively the refractive index of the third and fourthoptical units; and r₅ and 5₈ are respectively the radius of curvature ofthe third and fourth optical units.
 4. An optical system for use inilluminating an object comprising two optical units, the first opticalunit including a positive lens and having a convex rear surface, thesecond optical unit including a positive lens and having a convex frontand rear surfaces the optical system satisfying the following formulae:

    -3.0≦(d.sub.3 /r.sub.4)≦-0.3

    1.0f≦f.sub.2 ≦1.55f

where f is a synthesized focal length of the optical system; f₂ is thefocal length of the second optical unit; d₃ is the thickness of thesecond optical unit; and r₄ is the radius of curvature of the rearsurface of the second optical unit.
 5. An optical system for use inilluminating an object, comprising two optical units, the first opticalunit including a positive lens and having a convex rear surface thesecond optical unit including a positive lens and having a concave frontsurface and a convex rear surface, the optical system satisfying thefollowing formulae:

    -0.68≦{(1-n.sub.1)/r.sub.2 +(n.sub.3 -1)/r.sub.3 }f≦0.90

    0.67≦{(1-n.sub.3)/r.sub.4 }f

where f is the synthesized focal length of the optical system; r₂, r₃and r₄ are the radius of curvature of the rear surface of the firstoptical unit and of the front and rear surfaces of the second opticalunit, respectively; and n₁ and n₃ are the refractive indexes of thefirst and second optical units.
 6. An illumination apparatus forilluminating an object comprising:a light source; a first optical systempassing light from the light source to the original, said optical systemincluding a plurality of element lenses which are formed into fly's eyeconfiguration; an original to be illuminated; a second optical systempassing the light transmitted through the original; and a recordingmedium recording thereon the image of the original illuminated, whereinsaid first optical system comprises an entrance pupil for receivinglight from the light source, an exit pupil for passing the lightreceived to the object and an optical axis which extends to the lightsource and the recording medium, respectively, through the opticalsystem, the relationship among an incident height h at the entrancepupil, an illumination height H on the object, and a changing rate(dh/dH) of the incident height and the illumination height being definedby a function f(H):

    f(H)=(h/H)(dh/dH)

the optical system being designed so as to satisfy the following formulain the peripheral area of the object:

    f(0)≦f(H)

f(0) represented by the formula:

    f(0)-[fa'/{(a'-f)b'}[.sup.2

where a' is the distance between the light source and the primaryprincipal point of the optical system, and b' is the distance betweenthe real image of the light source and the object.